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Proportional Parts/Areas/Volumes

Proportional Parts/Areas/Volumes. During this lesson, you will: Determine measures of corresponding parts of similar triangles Determine ratios of areas in similar polygons (or circles) Determine ratios of volumes in similar polygons (or circles).

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Proportional Parts/Areas/Volumes

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  1. Proportional Parts/Areas/Volumes During this lesson, you will: Determine measures of corresponding parts of similar triangles Determine ratios of areas in similar polygons (or circles) Determine ratios of volumes in similar polygons (or circles) Geometry

  2. PART 1: Corresponding Parts of Similar Triangles VOCABULARY REVIEW Before we start, sketch and label the indicated part in each triangle below: Angle bisector 0X H X M Geometry

  3. Proportional Parts Theorem Proportional Parts Theorem: If two triangles are similar, then the corresponding ________, _________, and _____________ are __________to the corresponding sides. altitudes medians angle bisectors proportional Geometry

  4. CA = AP = CP = CL DA AY DY DF 35 = AP = CP = 25 21 AY DY DF 5 = AP = CP = 25 3 AY DY DF EXAMPLE: 15 Geometry

  5. Part 2: Proportions with Area Proportional Area Theorem: If two polygons (or circles) have corresponding sides (or radii) in the ration of m/n, then their areas are in the ratio of ______. m2/n2 Geometry

  6. EXAMPLES: • The ratio of the areas of two similar triangles is in the ratio of 4:9. What is the ratio of their altitudes? • The ratio of the medians of two similar triangles is 4:5. What is the ratio of their areas? Geometry

  7. Part 3: Proportions with Volume Proportional Volume Theorem: If two similar solids have corresponding dimensions in the ratio of m/n, then their volumes are in the ratio of ______. m3/n3 Geometry

  8. EXAMPLES: • The surface areas of two cubes are in the ratio of 25: 64. What is the ratio of their volumes? • The ratio of the weights of two spherical steel balls is 27:64. What is the ratio of the diameters of the steel balls? Geometry

  9. HOMEWORK ASSIGNMENT: Day 1: Proportional Parts WS Day 2: Proportional Area WS Day 3: Proportional Volume WS Geometry

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